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\author{Group 2\\ Stefan van der Horst, Martin Noy, Guilherme Soares Almeida, Julia Hofmockel}

\title{\Huge The bomber-battleship problem\\ \Large Master Operation Research, Year 1, Project 2\\ \small Department of Knowledge Engineering, Faculty of Humanities and Sciences, Maastricht University}

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\begin{abstract} 
In the bomber-battleship problem a bomber has one bomb and tries to hit a ship, 
which is traveling around. The problem is that there is a time lag between the moment 
the bomber drops the bomb and the moment the bomb explodes.

The main goal is to find strategies for the ship which minimize and for the bomber which maximize the probability that the ship is hit. 
These strategies differ when the time lag changes or when the ship can stay at a node or not. 
Only for the two-move lag optimal strategies for both can be found. For the three-move lag and for the situation where the ship can stay 
still, a bomber observes the ship's movements and calculates the probabilities of where it will be when the bomb explodes. For the ship some different strategies 
are developed, which try to reduce the hit rate.  

Another topic is the construction of a simple discrete time, continuous state model, 
where the ship moves in the plane and the bomber hits anything within a radius from the bombed point. 
The ship moves randomly through the plane, conditioned by some restrictions to simulate realistic movement. 
The bomber observes the movements and uses this information to decide where to drop the bomb. 
The continuous state model is also converted into a hidden Markov model with three states and three emissions, where the ship behaves according to the 
hidden Markov model and the bomber tries to detect it.
  
This research is done by first year students of the master Operations Research at Maastricht University.


\end{abstract}

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